SSC CGL Tier 1 2023 General Intelligence & Reasoning Questions with Solutions

Explanation

The letter-series is organized into four groups of five letters each, where each group begins with the constant prefix FGH. The remaining two positions in each group are filled by the letter Y and a sequential variable letter starting from T.

In the first three groups, the alphabetical variable (T, U, V) occupies the fourth position and Y occupies the fifth position, creating the blocks FGHTY, FGHUY, and FGHVY. In the fourth group, the letter Y occupies the fourth position and the next variable in the sequence, W, occupies the fifth position, forming the block FGHYW.

Placing the letters from the option TFHGVHY into the blanks in order completes this pattern: Group 1: F G H (T) Y Group 2: (F) G (H) U Y Group 3: F (G) H (V) Y Group 4: F G (H) (Y) W

This sequence maintains the FGH prefix for every block while completing the T-U-V-W progression.

Explanation

The numbers in the given sets follow the logic: n₂ = 2 × (n₁ + n₃) - 8.

Applying this formula to the provided sets: Set 1: (4, 16, 8) 2 × (4 + 8) - 8 = 2 × 12 - 8 = 24 - 8 = 16

Set 2: (2, 14, 9) 2 × (2 + 9) - 8 = 2 × 11 - 8 = 22 - 8 = 14

Applying the same logic to the set in option b: Set: (2, 8, 6) 2 × (2 + 6) - 8 = 2 × 8 - 8 = 16 - 8 = 8

The calculated value matches the second number in the set (2, 8, 6).

Explanation

The statements establish a hierarchical relationship where all ships are contained within the set of yachts, and all yachts are contained within the set of barges. This can be expressed as Ship ⊆ Yacht ⊆ Barge. Since all ships are barges, it logically follows that some barges are ships, which validates Conclusion I.

The statement "Some boats are ships" indicates a non-empty intersection between the set of boats and the set of ships. Because every ship is also a yacht and every yacht is also a barge, any entity that is both a boat and a ship must necessarily be a yacht and a barge as well. This confirms that there is an intersection between boats and yachts, and between boats and barges, making both Conclusion II (Some barges are boats) and Conclusion III (Some yachts are boats) logically certain. Since all three conclusions are derived directly from these subset relationships and intersections, all conclusions follow.

Explanation

The coding logic involves splitting the 8-letter word into two equal halves of four letters each. For each half, every letter is incremented by 1 according to its position in the English alphabet (L → L+1), and then the sequence of those four incremented letters is reversed.

Applying this to the word INTEREST: First half: INTE Incrementing each letter (I+1=J, N+1=O, T+1=U, E+1=F) gives the sequence JOUF. Reversing this sequence results in FUOJ.

Second half: REST Incrementing each letter (R+1=S, E+1=F, S+1=T, T+1=U) gives the sequence SFTU. Reversing this sequence results in UTFS.

Combining the two processed halves yields the final code: FUOJUTFS.

Explanation

The relationship between the letter-clusters follows a specific subtraction pattern based on the positions of letters in the English alphabet. For each analogy pair, the second letter-cluster is derived from the first by subtracting 3 from the first letter's position, 2 from the second letter's position, and 3 from the third letter's position.

In the first pair EKH : BIE, the positions change as follows: E (5) - 3 = B (2) K (11) - 2 = I (9) H (8) - 3 = E (5)

In the second pair MGP : JEM, the positions change as follows: M (13) - 3 = J (10) G (7) - 2 = E (5) P (16) - 3 = M (13)

To find the fifth letter-cluster that relates to QDI, we apply the reverse operation or solve for the unknown positions X₁X₂X₃ using the same pattern: X₁ - 3 = Q (17) ⟹ X₁ = 20 (T) X₂ - 2 = D (4) ⟹ X₂ = 6 (F) X₃ - 3 = I (9) ⟹ X₃ = 12 (L)

The resulting letters at positions 20, 6, and 12 are T, F, and L.

Explanation

In the given set (2, 50, 500), the numbers are related following the multiplication of the first two numbers by a constant factor of 5: Third Number = (First Number × Second Number) × 5

Applying the values from the set: (2 × 50) × 5 = 100 × 5 = 500

This logic establishes the relationship between the numbers in the selected set, where the product of the first two terms multiplied by 5 yields the third term.

Explanation

The second statement specifies that some yellow are buses. In categorical logic, a particular affirmative proposition of the form Some A are B can be logically converted into the form Some B are A. This principle of conversion ensures that the relationship between the two categories is reciprocal. Therefore, the fact that some yellow items are categorized as buses necessitates that some buses are also categorized as yellow. This makes conclusion II a direct and valid logical derivation from the given statements.

Explanation

The series follows a consistent arithmetic pattern for each letter position within the triplets. By converting the letters to their corresponding numerical positions in the alphabet where A=1 and Z=26:

For the first letter of each term, the pattern is an increment of +2: Z(26) + 2 = B(2), B(2) + 2 = D(4), D(4) + 2 = F(6), and so on.

For the second letter of each term, the pattern is an increment of +4: B(2) + 4 = F(6), F(6) + 4 = J(10), J(10) + 4 = N(14), and so on.

For the third letter of each term, the pattern is a decrement of -5: Q(17) - 5 = L(12), L(12) - 5 = G(7), G(7) - 5 = B(2), and B(2) - 5 = W(23) through alphabetical wraparound (26 - 3 = 23).

Applying these transformations to the second term BFL, the first letter is B(2) + 2 = D, the second letter is F(6) + 4 = J, and the third letter is L(12) - 5 = G. Combining these results gives the missing term DJG.

Explanation

The logic followed in the given sets (a, b, c) is (a × b) + (a + b) = c, which can also be expressed as (a + 1) × (b + 1) - 1 = c.

For the set (10, 5, 65): (10 × 5) + (10 + 5) = 50 + 15 = 65

For the set (9, 8, 89): (9 × 8) + (9 + 8) = 72 + 17 = 89

Applying the same logic to the numbers in option c (4, 5, 29): (4 × 5) + (4 + 5) = 20 + 9 = 29

Explanation

To arrange the words in dictionary order, they must be compared letter by letter from left to right. All six words begin with the prefix BRE. Comparing the fourth letter, Breakdown (1), Breathe (3), and Breakfast (6) contain the letter A, which precedes the letter E found in Breeding (4) and Breeze (5), and the letter V in Brevity (2).

Within the group starting with BREA, we compare the fifth letters: Breakdown (1) and Breakfast (6) have K, while Breathe (3) has T. Since K comes before T, words 1 and 6 must precede 3. To differentiate between Breakdown and Breakfast, we look at the sixth letter; D in Breakdown comes before F in Breakfast, establishing the order 1, 6, 3.

Next, comparing the words starting with BREE, the fifth letter of Breeding (4) is D, and the fifth letter of Breeze (5) is Z. Since D appears before Z in the alphabet, 4 precedes 5. Finally, Brevity (2) is placed last as its fourth letter V comes after A and E. Combining these sequences yields the final dictionary order: 1, 6, 3, 4, 5, 2.

Explanation

The cluster JOH is the odd one out because its first two letters do not form an alphabetical opposite pair. For two letters to be opposites, the sum of their numerical positions in the English alphabet must equal 27. In this case, J is the 10th letter and O is the 15th letter, yielding a sum of 25. While the third letter H correctly follows a shift of minus two from the first letter (10 - 2 = 8), the failure to satisfy the opposite-pair rule for the first two characters identifies this cluster as the exception to the rule governing the group.

Explanation

The pattern followed in the given sets is 2 × First Number - Second Number = Third Number.

In the first set (6, 4, 8), applying the logic gives 2 × 6 - 4 = 12 - 4 = 8. In the second set (17, 6, 28), applying the logic gives 2 × 17 - 6 = 34 - 6 = 28.

Applying this relationship to the set in option d, (13, 5, 21), we find 2 × 13 - 5 = 26 - 5 = 21.

Explanation

The series progresses according to a fixed numerical shift for each letter position in the triplets.

For the first letters, the sequence follows a -4 pattern: X(24) → T(20) → P(16) → L(12). Continuing this subtraction, 12 - 4 = 8, which is the position for the letter H.

For the second letters, the sequence follows a +4 pattern: G(7) → K(11) → O(15) → S(19). Continuing this addition, 19 + 4 = 23, which is the position for the letter W.

For the third letters, the sequence follows a -4 pattern: R(18) → N(14) → J(10) → F(6). Continuing this subtraction, 6 - 4 = 2, which is the position for the letter B.

Applying these shifts to the fourth term LSF results in the characters H, W, and B. This pattern remains consistent through to the final term DAX, as H(8) - 4 = D(4), W(23) + 4 = 27 ≡ A(1), and B(2) - 4 = -2 ≡ X(24) in the cyclic alphabet.

Explanation

The numbers in the given sets follow an arithmetic progression with a constant common difference of 13. In the first set (15, 28, 41), the differences are 28 - 15 = 13 and 41 - 28 = 13. Similarly, in the second set (19, 32, 45), the differences are 32 - 19 = 13 and 45 - 32 = 13.

Applying the same logic to the numbers in the set (22, 35, 48): 35 - 22 = 13 48 - 35 = 13

The relationship n₂ - n₁ = 13 and n₃ - n₂ = 13 is satisfied, making it the set that follows the identical pattern.

Explanation

The expression E = F = G H = I can be broken down using the provided definitions. The relation E = F indicates that E is the sister of F, and F = G indicates that F is the sister of G. These two relations establish that E, F, and G are all siblings of the same parentage. The relation G H defines G as the father of H, which confirms that G is male. Since G is the male sibling of E, the relationship of G to E is that of a brother.

Explanation

The coding logic involves reversing the order of the first seven letters of the word while keeping the eighth letter in its original position at the end. In the word PRECIOUS, the first seven letters PRECIOU are reversed to UOICERP, and the final letter S remains at the end, resulting in UOICERPS. Similarly, for FLAGRANT, the first seven letters FLAGRAN are reversed to NARGALF, and the final letter T remains at the end to form NARGALFT. Applying this pattern to CHILDISH, the first seven letters CHILDIS are reversed to become SIDLIHC, and the last letter H is kept in its place at the end, producing the code SIDLIHCH.

Explanation

The relationship between the given words is that of a Tool and its primary Function. A shovel is an instrument specifically designed for the action of scooping materials like earth, snow, or coal. Similarly, a spanner is a mechanical tool used to provide a secure grip and apply torque for turning or holding objects such as nuts and bolts. Both pairs follow the logic where the first noun is an implement and the second verb describes the specific action it is meant to perform.

Explanation

The letters in the clusters follow a numerical pattern based on their positions in the English alphabet where A=1, B=2, …, Z=26. In the clusters ABEJ, Tuxc, and VWzE, the positions increase by consecutive odd numbers: +1, +3, and +5. For example, in ABEJ, the positions are 1, 2 (1+1), 5 (2+3), and 10 (5+5).

In the cluster FGJP, the alphabetical positions are F=6, G=7, J=10, and P=16. Calculating the differences between consecutive letters gives 7 - 6 = 1, 10 - 7 = 3, and 16 - 10 = 6. While the first two increments follow the pattern, the final increment is +6 instead of the +5 found in the other clusters. This deviation in the final letter's position makes FGJP the odd one out.

Explanation

To make the equation (31 × 3) - (27 × 4) + (81 ÷ 9) = 126 correct, we interchange the numbers 27 and 9 and the signs + and -. After the interchange, the new equation is:

(31 × 3) + (9 × 4) - (81 ÷ 27) = 126

Following the BODMAS rule, we first solve the operations within the parentheses: 31 × 3 = 93 9 × 4 = 36 81 ÷ 27 = 3

Now substitute these values back into the equation: 93 + 36 - 3 = 126

Adding 93 and 36: 129 - 3 = 126

Subtracting 3 from 129: 126 = 126

The left-hand side equals the right-hand side, confirming that interchanging 27 and 9 along with + and - correctly balances the equation.

Explanation

The mathematical pattern governing the number-pairs is that the first number is equal to the square of twice the second number, expressed by the formula x = (2y)². For the pair 186:7, applying this operation to the second number gives (2 × 7)² = 14² = 196. Since the first number provided is 186 instead of 196, this pair does not satisfy the established logic and is the odd one out.

Explanation

To arrange words in dictionary order, we compare them letter by letter from left to right. All six words begin with the prefix Abs. The fourth letters are o in Absolutely and Absorber, t in Abstain, Abstract, and Abstriction, and u in Absurdly. Since o comes before t and u in the alphabet, the words starting with Abso come first. Between Absolutely and Absorber, the fifth letter l in Absolutely precedes the fifth letter r in Absorber, placing 4 before 6.

Next, we look at the words starting with Abst. The fifth letter in Abstain is a, while the fifth letter in both Abstract and Abstriction is r. Since a precedes r, Abstain (5) comes next. Comparing Abstract and Abstriction, both share the first six letters Abstra, but the seventh letter a in Abstract comes before the seventh letter i in Abstriction, placing 3 before 2. Finally, Absurdly (1) is placed last because its fourth letter u follows o and t. Following this alphabetical sequence, the correct order is 4, 6, 5, 3, 2, 1.

Explanation

The numerical relationship follows the pattern y = 3x³, where y is the first term and x is the second term in each pair.

In the first pair 24:2: 3 × 2³ = 3 × 8 = 24

In the second pair 81:3: 3 × 3³ = 3 × 27 = 81

Applying this same logic to the third pair 375:?: 3 × x³ = 375 x³ = ³⁷⁵⁄₃ x³ = 125 x = ³√(125) = 5

Explanation

By comparing the phrases, we can isolate the code for each word. Comparing meet them now (el cn ah) and never meet alone (cn sm uv), the common word meet corresponds to the common code cn. Comparing meet them now (el cn ah) and not alone now (ah sm rt), the common word now corresponds to the common code ah. Since meet is cn and now is ah, the remaining word in the first phrase them must be el.

Comparing never meet alone (cn sm uv) and not alone now (ah sm rt), the common word alone corresponds to the common code sm. In the phrase not alone now (ah sm rt), we already identified now as ah and alone as sm, so the remaining word not must be rt. Combining the codes for not and them, we get rt and el.

Explanation

By interchanging the numbers 4 and 20, the given equation 5 × 15 ÷ 3 + 20 - 9 = 4 is modified to 5 × 15 ÷ 3 + 4 - 9 = 20. Following the BODMAS rule, the operations are carried out in the sequence of division, multiplication, addition, and then subtraction.

The division 15 ÷ 3 gives 5, making the equation 5 × 5 + 4 - 9 = 20. Performing the multiplication, 5 × 5 results in 25, leading to 25 + 4 - 9 = 20. Adding 25 and 4 yields 29, and finally, subtracting 9 from 29 results in 20. Since the calculation of the left-hand side equals the value on the right-hand side, the interchange of 4 and 20 makes the equation correct.

Explanation

The series consists of 16 character positions including the blanks. By dividing the series into four equal groups of four letters each, the structure appears as D _ B A | _ C B _ | D C B _ | D _ B A. To establish a consistent repeating pattern, each segment must be identical. Placing the letters C, D, A, A, and C into the blanks sequentially transforms every group into the four-letter block DCBA. The resulting complete series is DCBA DCBA DCBA DCBA, which follows a perfectly uniform and repetitive sequence.

Explanation

The series follows a pattern based on increasing differences between consecutive terms. First, calculate the differences between the given numbers: 37 - 31 = 6 46 - 37 = 9 60 - 46 = 14 81 - 60 = 21

Next, examine the second-level differences (the difference between the differences): 9 - 6 = 3 14 - 9 = 5 21 - 14 = 7

The second-level differences are consecutive odd numbers starting from 3, which are 3, 5, 7, …. Following this pattern, the next second-level difference must be 9. Adding this to the last first-level difference gives 21 + 9 = 30. To find the missing number in the original series, add this value to the last known term: 81 + 30 = 111.

Explanation

The logic followed in the given sets is that the third number is the sum of seven times the first number and the second number. This can be expressed by the formula:

(First Number × 7) + Second Number = Third Number

Applying this to the first provided set (28, 65, 261): (28 × 7) + 65 = 196 + 65 = 261

Applying this to the second provided set (37, 83, 342): (37 × 7) + 83 = 259 + 83 = 342

In option b (46, 92, 414), the same mathematical relationship is maintained: (46 × 7) + 92 = 322 + 92 = 414

Explanation

The pattern follows a two-step process: first, the letters of the word are reversed, and then consecutive natural numbers starting from 1 are added to the positional values of those reversed letters.

In the case of ORANGE, reversing the string gives EGNARO. Adding +1, +2, +3, +4, +5, +6 to the alphabetical positions of these letters results in 5+1=6 (F), 7+2=9 (I), 14+3=17 (Q), 1+4=5 (E), 18+5=23 (W), and 15+6=21 (U), which forms FIQEWU.

For MANGO, the reversed string is OGNAM. Adding +1, +2, +3, +4, +5 to the positions yields 15+1=16 (P), 7+2=9 (I), 14+3=17 (Q), 1+4=5 (E), and 13+5=18 (R), which forms PIQER.

Applying this logic to APPLE, the word is first reversed to get ELPPA. Adding the incremental values to the positions results in: E (5) + 1 = 6 (F) L (12) + 2 = 14 (N) P (16) + 3 = 19 (S) P (16) + 4 = 20 (T) A (1) + 5 = 6 (F)

The resulting letter-cluster is FNSTF.

Explanation

To verify the equation, we substitute the numbers 14 and 6 and interchange the signs + and - in the given expression 784 ÷ 6 × 9 - 30 + 14 = 528. The modified equation becomes:

784 ÷ 14 × 9 + 30 - 6 = 528

Applying the BODMAS rule, we perform the operations in sequence:

First, solve the division: 784 ÷ 14 = 56

Next, perform the multiplication: 56 × 9 = 504

Finally, perform the addition and subtraction: 504 + 30 - 6 = 534 - 6 = 528

The left-hand side equals the right-hand side, confirming that the interchanges result in a correct equation.

Explanation

All six words begin with the prefix Mon. To arrange them in dictionary order, we compare the fourth letter of each word. In Monitor (5), the fourth letter is i, which alphabetically precedes the fourth letters o, s, and u found in the other words, placing it first. Next, we compare Monopoly (3) and Monorail (1), which both have o as their fourth letter; Monopoly comes before Monorail because its fifth letter p precedes r. Following these are the words starting with Mons: Monsoon (6) comes before Monster (4) because its fifth letter o precedes t. Finally, Monument (2) is placed last because its fourth letter u is alphabetically the latest. This comparison yields the sequence 5, 3, 1, 6, 4, 2.

Explanation

The logic followed in the given letter-clusters is to divide the six-letter word into two equal halves of three letters each and reverse the sequence of letters within each half.

In the first pair, DISMAY is split into DIS and MAY. Reversing DIS gives SID, and reversing MAY gives YAM, resulting in the cluster SIDYAM.

In the second pair, DRIVER is split into DRI and VER. Reversing DRI gives IRD, and reversing VER gives REV, resulting in the cluster IRDREV.

Following the same pattern for SAFARI, the word is split into SAF and ARI. Reversing the first half SAF results in FAS, and reversing the second half ARI results in IRA. Combining these two halves gives the letter-cluster FASIRA.

Explanation

To determine the relationship, the statement can be broken down step by step from Rajan's perspective. Rajan's wife's son is Rajan's own son. The father of Rajan's son is Rajan himself. Rajan's father's mother is Rajan's mother. The husband of Rajan's mother is Rajan's father. Finally, the daughter of Rajan's father is Rajan's sister. Therefore, the girl in the photo is Rajan's sister.

Explanation

The relationship between pens and books is not definitively established by the statements. Conclusion I (Some books are pens) is a particular affirmative statement, and Conclusion III (No book is a pen) is a universal negative statement. These two conclusions share the same subject (books) and predicate (pens). In syllogistic logic, when two conclusions are individually uncertain but form a pair of particular affirmative (I) and universal negative (E) with the same terms, they constitute a complementary pair. Since it is logically impossible for both to be false simultaneously—either there is at least one book that is a pen or there are absolutely no books that are pens—the either-or rule applies. Conclusion II does not follow because the overlap between newspapers and novels does not necessitate an overlap between pens and novels.

Explanation

The numbers in the given sets (9, 20, 31) and (38, 49, 60) follow an arithmetic progression where the common difference between consecutive terms is constant. In the first set, the difference is 20 - 9 = 11 and 31 - 20 = 11. In the second set, the difference is 49 - 38 = 11 and 60 - 49 = 11. This relationship can be expressed by the property a + c = 2b, where a, b, and c represent the first, second, and third numbers respectively. Applying this to the first set: 9 + 31 = 40, which is 2 × 20. Applying it to the second set: 38 + 60 = 98, which is 2 × 49. The set (14, 24, 34) exhibits the same relationship as the difference between consecutive terms is a constant 10 (24 - 14 = 10 and 34 - 24 = 10). Substituting these values into the formula, 14 + 34 = 48, which is equal to 2 × 24.

Explanation

The pattern followed in the given sets is that the sum of the first and third numbers, when multiplied by 5, yields the middle number.

Pattern: (First Number + Third Number) × 5 = Second Number

Applying this to the first set (7, 150, 23): (7 + 23) × 5 = 30 × 5 = 150

Applying this to the second set (11, 75, 4): (11 + 4) × 5 = 15 × 5 = 75

Similarly, in option d, for the set (15, 140, 13): (15 + 13) × 5 = 28 × 5 = 140

Explanation

The code for each word is determined by the sum of the positional values of its letters in the English alphabet, where A=1, B=2, ..., and Z=26.

For the word RAT: R = 18, A = 1, T = 20 Sum = 18 + 1 + 20 = 39

For the word MICE: M = 13, I = 9, C = 3, E = 5 Sum = 13 + 9 + 3 + 5 = 30

Following the same logic for ZEBRA: Z = 26, E = 5, B = 2, R = 18, A = 1 Sum = 26 + 5 + 2 + 18 + 1 = 52

Explanation

The cluster DCB follows a pattern of consecutive reverse alphabetical order. Mapping the letters to their numerical positions in the English alphabet, we get D = 4, C = 3, and B = 2. The logic applied here is a constant difference of 1 between each adjacent letter: 4 - 3 = 1 and 3 - 2 = 1. This makes it the odd one out because it deviates from the general rule of the set, which involves a difference of 1 between the first two letters and a difference of 2 between the second and third letters.

Explanation

The given series follows a distinct pattern for each letter position in the clusters. In the first position, letters increase by 2 (B to D to F to H to J). In the second position, letters decrease by 2 (Z to X to V to T to R). In the third position, letters increase by 1 (V to W to X to Y to Z). In the fourth position, letters decrease by 1 (R to Q to P to O to N). Following these progressions from the second term DXWQ, the first letter D+2 gives F, the second letter X-2 gives V, the third letter W+1 gives X, and the fourth letter Q-1 gives P. This results in the cluster FVXP.

Explanation

The series consists of 16 characters which can be divided into four groups of four letters each. By observing the sequence, a repeating pattern of ZYRR is identified.

When the letters from the selected option are placed in the blanks, the series becomes ZYRR | ZYRR | ZYRR | ZYRR. The first blank takes R to complete the first ZYRR unit. The second blank takes Y to complete the second ZYRR unit. The third blank takes R to complete the third ZYRR unit. The fourth and fifth blanks take Z and R respectively to complete the final ZYRR unit. This sequence of inserted letters R, Y, R, Z, R forms the correct pattern.

Explanation

The logic governing these number-pairs is that the first number x is equal to twice the square of the second number y, expressed as x = 2y². Applying this rule to the second number 15 results in 2 × 15² = 2 × 225 = 450. Since the first number in this pair is 350 instead of 450, it does not conform to the mathematical operation followed by the rest of the set.

Explanation

The pattern follows a row-wise logic where the third number is obtained by adding the first number, the second number, and one-fourth of the first number. The mathematical relationship can be expressed as C3 = C1 + C2 + (C1 ÷ 4).

In the first row, the calculation is 16 + 15 + (16 ÷ 4) = 31 + 4 = 35. In the second row, the calculation is 12 + 18 + (12 ÷ 4) = 30 + 3 = 33. Following this established logic for the third row, we perform the operation 8 + 17 + (8 ÷ 4) = 25 + 2 = 27.

Explanation

The numerical relationship between the pairs follows the formula x = 3y³, where y is the second number and x is the first number. In the first pair 1029:7, substituting the second number gives 3 × 7³ = 3 × 343 = 1029. In the second pair 2187:9, the same logic applies as 3 × 9³ = 3 × 729 = 2187. To find the value related to the fifth number 24, we use the equation 24 = 3 × y³. Dividing both sides by 3 results in y³ = 8, and the cube root of 8 is 2.

Explanation

Applying the given rules to the word FOREFOOT: F (Consonant) becomes E (previous letter) O (Vowel) becomes P (following letter) R (Consonant) becomes Q (previous letter) E (Vowel) becomes F (following letter) F (Consonant) becomes E (previous letter) O (Vowel) becomes P (following letter) O (Vowel) becomes P (following letter) T (Consonant) becomes S (previous letter)

The newly formed word is EPQFEPPS. The second alphabet from the left is P and the first alphabet from the right is S. In the English alphabetical series, the letters between P and S are Q and R. Counting these, we find there are exactly two alphabets between them.

Explanation

The given series follows a pattern where each term is increased by a consecutive prime number starting from 11. Calculating the differences between the known terms reveals this sequence: the difference between 38 and 27 is 11, the difference between 87 and 68 is 19, and the difference between 110 and 87 is 23. The prime numbers between 11 and 19 are 13 and 17. By adding the next consecutive prime number, 13, to the second term, we get 38 + 13 = 51. Verification with the subsequent term shows 51 + 17 = 68, which matches the given series. Thus, the differences follow the prime number sequence 11, 13, 17, 19, 23.

Explanation

The code language follows a pattern based on the reverse alphabetical positions of the letters. In this system, Z is 1, Y is 2, and A is 26. For each letter, its reverse positional value is determined, and if the value is a two-digit number, the digits are added together to form a single-digit code.

For CAKE: C is the 24th letter from the end, and 2+4=6. A is the 26th letter from the end, and 2+6=8. K is the 16th letter from the end, and 1+6=7. E is the 22nd letter from the end, and 2+2=4. Thus, CAKE is 6874.

For EASY: E is the 22nd letter from the end, and 2+2=4. A is the 26th letter from the end, and 2+6=8. S is the 8th letter from the end, which remains 8. Y is the 2nd letter from the end, which remains 2. Thus, EASY is 4882.

For MAKE: M is the 14th letter from the end, and 1+4=5. A is the 26th letter from the end, and 2+6=8. K is the 16th letter from the end, and 1+6=7. E is the 22nd letter from the end, and 2+2=4. The resulting code for MAKE is 5874.

Explanation

By interchanging the signs - and ÷, the original expression 3 × 12 - 6 ÷ 2 + 12 transforms into:

3 × 12 ÷ 6 - 2 + 12

Following the BODMAS rule, first perform the division: 12 ÷ 6 = 2

Then perform the multiplication: 3 × 2 = 6

Finally, solve the remaining addition and subtraction from left to right: 6 - 2 + 12 = 4 + 12 = 16

The resulting value matches the right-hand side of the equation.

Explanation

The coding pattern involves reversing the word and then applying an alternating subtraction of 3 and 2 to the alphabetical positions of the letters.

For MOBILE: Reverse the letters to get ELIBOM. E (5) - 3 = 2 (B) L (12) - 2 = 10 (J) I (9) - 3 = 6 (F) B (2) - 2 = 0/26 (Z) O (15) - 3 = 12 (L) M (13) - 2 = 11 (K) The code is BJFZLK.

For TABLET: Reverse the letters to get TELBAT. T (20) - 3 = 17 (Q) E (5) - 2 = 3 (C) L (12) - 3 = 9 (I) B (2) - 2 = 26 (Z) A (1) - 3 = -2 ≡ 24 (X) T (20) - 2 = 18 (R) The code is QCIZXR.

Following the same logic for KINDLE: Reverse the letters to get ELDNIK. E (5) - 3 = 2 (B) L (12) - 2 = 10 (J) D (4) - 3 = 1 (A) N (14) - 2 = 12 (L) I (9) - 3 = 6 (F) K (11) - 2 = 9 (I) The resulting code is BJALFI.

Explanation

The series follows a consistent mathematical pattern for each letter position within the clusters.

First letter: The sequence increases by one position in the alphabet. B +1 C +1 D +1 E +1 F.

Second letter: The sequence decreases by two positions in the alphabet. Starting from A (which can be treated as 27 in a 1-26 cycle), the pattern is A -2 Y -2 W -2 U -2 S.

Third letter: The sequence increases by three positions in the alphabet. W +3 Z +3 C +3 F +3 I. Note that Z is the 26ᵗʰ letter, and adding 3 to it results in 29, which wraps around to the 3ʳᵈ letter, C.

Fourth letter: The sequence decreases by four positions in the alphabet. P -4 L -4 H -4 D -4 Z. Here, P is the 16ᵗʰ letter, and 16 - 4 = 12, which corresponds to L.

Combining these transformations, the cluster following BAWP is CYZL.

Explanation

To make the equation correct, we apply the interchanges specified in option b: 12 and 38, and the signs × and -. Substituting these into the original equation 840 ÷ 38 - 7 + 10 × 12 = 462, we get the new expression:

840 ÷ 12 × 7 + 10 - 38

Applying the BODMAS rule, we perform division first:

840 ÷ 12 = 70

Next, we perform the multiplication:

70 × 7 = 490

Finally, we perform addition and subtraction from left to right:

490 + 10 - 38 = 500 - 38 = 462

The calculated result 462 matches the right-hand side of the equation.

Explanation

To arrange words in dictionary order, we compare them letter by letter from left to right. All five words begin with the letters T-Y. For the third letter, Typographical, Typologically, Typifications, and Typicalness all have P, while Tyrannosaurus has R. Since P comes before R in the alphabet, Tyrannosaurus (5) will be the last word in the sequence. Among the remaining four words, we compare the fourth letter. Typicalness (4) and Typifications (3) have I, whereas Typographical (1) and Typologically (2) have O. As I precedes O, we look at the fifth letter of words 4 and 3. Typicalness has C and Typifications has F. Since C comes before F, the order is Typicalness (4) followed by Typifications (3). For words 1 and 2, the fifth letters are G and L respectively. Since G comes before L, Typographical (1) precedes Typologically (2). Combining these steps, the final dictionary order is 4, 3, 1, 2, 5.